In a particular country on the African continent, 35% of the

hunterofdeath63

hunterofdeath63

Answered question

2021-12-13

In a particular country on the African continent, 35% of the population is estimated to have at least one smart phone. If a small sample of 40 people is selected from the population for a statistical investigation, Use the Binomial distribution to estimate the probability of the number of people in the sample that have at least one smart phone is;
a) at most 15;
b) more than 12 but fewer than 18;
c) exactly equal to the mean of the distribution

Answer & Explanation

chumants6g

chumants6g

Beginner2021-12-14Added 33 answers

Step 1
Let X denote the number of people having at least one smartphone
Then given that:
XBinomial(n=40,p=0.35)
a) The required probability is:
P(X15)=0.694664
which is calculated using Excel function:
=BINOM.DIST(15,40,0.35,TRUE)
b) The required probability is:
P(12<X<18)=P(X<18)P(X<12)
=0.615767
which is calculated using Excel function:
=BINOM.DIST(18,40,0.35,TRUE)-BINOM.DIST(12,40,0.35,TRUE)
Step 2
c) Mean of the distribution is =n×p=40×0.35=14
So, P(X=14)=0.131316
which is calculated using Excel function:
=BINOM.DIST(14,40,0.35,FALSE)

Bernard Lacey

Bernard Lacey

Beginner2021-12-15Added 30 answers

Step 1
p=0.35
n=40
q=p1=0.65
P(X=x)=Cxnpxqnx
a) P(X15)=x=015Cx40(0.35)x(0.65)40x
P(X15)=0.6946
b) P(12<C<18)=1317Cx40(0.35)x(0.65)40x
=x=017Cx40(0.35)x(0.65)40xx=012Cx40(0.35)x(0.65)40x
=0.87610.3143
=0.5618
c) Mean=np=40×0.35=14
P(X=14)=C1440(0.35)14(0.65)26
P(X=14)=0.1313

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